Methanol (CH3OH) is one of the most abundant interstellar molecules, offering a vast number of transitions to be studied, including many maser lines. However, while the strongest Galactic CH3OH lines, the so-called class II masers, show no indications for the presence of superluminous counterparts in external galaxies, the less luminous Galactic class I sources appear to be different. Here we report class I 36 GHz (lambda approximate to 0.8 cm) CH3OH 4(-1) -> 3(0) E line emission from the nearby galaxies Maffei 2 (D approximate to 6 Mpc) and IC 342 (D approximate to 3.5 Mpc), measured with the 100 m telescope at Effelsberg at three different epochs within a time span of about five weeks. The 36 GHz methanol line of Maffei 2 is the second most luminous among the sources detected with certainty outside the Local Group of galaxies. This is not matched by the moderate infrared luminosity of Maffei 2. Higher-resolution data are required to check whether this is related to its prominent bar and associated shocks. Upper limits for M 82, NGC 4388, NGC 5728 and Arp 220 are also presented. The previously reported detection of 36 GHz maser emission in Arp 220 is not confirmed. Nondetections are reported from the related class I 44 GHz (lambda approximate to 0.7 cm) methanol transition towards Maffei 2 and IC 342, indicating that this line is not stronger than its 36 GHz counterpart. In contrast to the previously detected 36 GHz CH3OH emission in NGC 253 and NGC 4945, our 36 GHz profiles towards Maffei 2 and IC 342 are similar to those of previously detected nonmasing lines from other molecular species. However, by analogy to our Galactic center region, it may well be possible that the 36 GHz methanol lines in Maffei 2 and IC 342 are composed of a large number of faint and narrow maser features that remain spatially unresolved. In view of this, a search for a weak broad 36 GHz line component would also be desirable in NGC 253 and NGC 4945.